Cut carrots to roughly and same size and shape as the green beans. Simmer them in just enough water to cover 5-10 minutes, until done to your taste. (Time will vary, depending on size and shape.)
Add green beans, return to a boil and cook until done.
Stir miso into the cooking liquid until smooth. Stir the resulting sauce all through the vegetables, and serve.
Notes
If you are using fresh green beans, simply add them to the carrots a minute or two after the water has come to a simmer.